Vancouver, measured in minutes

In metres this is an ordinary map. In minutes every street slides along the line running out from the start, to a distance set by how long the trip takes. The direction a place lies in never changes. Only how far away it is.

The idea has a name. Geographers call the ordinary version absolute space, where distance is a property of the ground and does not care who you are. The other is relative space, where distance is whatever it costs you to cross it — in minutes here, but it could as easily be money, or effort, or risk. Neither is the true one. The whole point of putting them on one screen is that you can watch the same city be both.

There are two maps here and no map in between, so the change is shown as a movement rather than as a dial. Half way between metres and minutes would be half of one measurement added to half of another, which is not a way of measuring anything.

The map in minutes is true along the lines that run out from the start, and only along those. The gap you see between two places that are not the start is not their travel time, and nothing on this map can show it. That is the trade a map projection makes too: to get one thing right, it gives up the rest.

For more, see: David O’Sullivan, Computing Geographically (Guilford, 2024), Chapter 2 on relative space and Figure 6.14, which is a map of this kind for Santa Barbara. Alain L’Hostis & Farouk Abdou, “What is the shape of geographical time-space?”, ISPRS International Journal of Geo-Information 10(5), 340 (2021).

How steep a street is. A slope is written here as a rise over a run: 5 in 100 means the ground climbs five metres for every hundred you travel along it. That does not sound like much, and it is already the point at which a walkway has to be built as a ramp. Vancouver has plenty of streets at eight and ten. The heights come from a laser survey of the bare ground, so a street’s slope is the slope of the earth under it rather than of the buildings beside it.

Nobody’s trip is this fast. There are no traffic lights here, no queues, no waiting to cross, and no time spent parking. Every traveller on this page moves as if the way were clear, because there is no open record of Vancouver traffic that could say otherwise. It is the same assumption for all four, so comparing them is fair. What the map shows is how the ground and the network shape a trip, not how long the trip takes.

For more, see: Waldo Tobler, “Three presentations on geographical analysis and modeling”, NCGIA Technical Report 93-1 (1993), where the hiking function is W = 6 exp(−3.5 |S + 0.05|) km/h, with S the rise over the run. David Gordon Wilson & Theodor Schmidt, with contributions by Jim Papadopoulos, Bicycling Science (4th edn, MIT Press, 2020), chapter 4, for the power equation this simplifies. On the slope limit: 2010 ADA Standards for Accessible Design §403.3, and CSA B651, both of which set 1:20; a ramp may go to 1:12, and needs handrails once it rises past 150 mm.

Swapping the start with the blue pin is the test worth running. If getting there and getting back took the same time, the two maps would be the same map. They are not. One-way streets and hills both run one way, so the city is a different shape depending on which end of the trip you are standing at.

For more, see: David O’Sullivan, Computing Geographically (Guilford, 2024), Chapter 2: “It might take longer to travel from A to B than from B to A.”

The photograph is stretched by the same rule as the streets, so you can watch real ground pull apart. It is only stretched where the streets can say how long it takes to get there. Water and mountainside have no answer, so they stay where they are and fade out as the map turns to minutes.

That fading is the honest part. Interpolating a travel time across the inlet would make the water stretch like everything else, which would say the sea is merely slow. It is not slow. It is not there.

Turn it off if the streets are hard to read. On a projector, which crushes dark tones, plain often wins.

For more, see: the image is Copernicus Sentinel-2, 12 August 2025, at 10 m, washed out and lightened here so that street lines stay legible on top of it.